Expand the Trigonometric Expression 15(5)^2(-1/2x)^4

$15 {(5)}^{2} {(- \frac{1}{2} x)}^{4}$

Step 1

Simplify the expression.

Raise $5$ to the power of $2$ .

$15 \cdot 25 {(- \frac{1}{2} x)}^{4}$

Multiply $15$ by $25$ .

$375 {(- \frac{1}{2} x)}^{4}$

Step 2

Combine $x$ and $\frac{1}{2}$ .

$375 {(- \frac{x}{2})}^{4}$

Step 3

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- \frac{x}{2}$ .

$375 ({(- 1)}^{4} {(\frac{x}{2})}^{4})$

Apply the product rule to $\frac{x}{2}$ .

$375 ({(- 1)}^{4} \frac{x^{4}}{2^{4}})$

Step 4

Simplify the expression.

Raise $- 1$ to the power of $4$ .

$375 (1 \frac{x^{4}}{2^{4}})$

Multiply $\frac{x^{4}}{2^{4}}$ by $1$ .

$375 \frac{x^{4}}{2^{4}}$

Raise $2$ to the power of $4$ .

$375 \frac{x^{4}}{16}$

Step 5

Combine $375$ and $\frac{x^{4}}{16}$ .

$\frac{375 x^{4}}{16}$